Riemann intergability versus continuity for vector-valued functions


 Lone, Nisar A.  and  Chishti, T. A.


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The interplay between Riemann integrability and continuity is an interesting topic of modern analysis. In this paper, Riemann integrability of vector-valued continuous functions, property of Lebesgue and weak property of Lebesgue are surveyed and discussed. We also prove that \ell_1(\mathbb{N}, X) has the property of Lebesgue.

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 Lone, Nisar A. , Chishti, T. A.